Skip to main content
SpringerLink
Log in

Manifestations of Pauli exclusion principle in communication-theory of the chemical bond

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The implications of the Pauli exclusion principle for the entropy/informa- tion indices of the chemical bond formulated within the communication theory approach are explored. The spatial information channels in the local, two-electron resolution are derived for the singlet and triplet states of two electrons, modeling the chemical bonding and non-bonding states in a molecule, respectively. Their average conditional-entropy (covalency) and mutual-information (ionicity) descriptors are compared against those characterizing the separate atoms and an upper-bound to the information-theoretic bond-order for the molecular orbital “events” is determined. An illustrative application to AO channels in H2 generates numerical values of the information-theoretic indices for this prototype covalent bond. The molecular information systems are interpreted as the ensemble averages of the elementary deterministic (zero-covalency) information networks. Examples of such a channel synthesis include model binary channels and that representing the elementary valence-bond (VB) covalent structure in H2. The ensemble representation of the spin channel for the triplet state of two electrons, averaged over the three spin-projection components, offers an entropic perspective on the spin-pairing in the bond-formation process. The spin-paired (singlet) communication system is obtained by maximizing in the ensemble-average communication system of the triplet state the information-flow (ionicity) to its capacity level.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.A. Fisher, Proc. Cambridge Phil. Soc. 22, 700 (1925); see also: B.R. Frieden, Physics from the Fisher Information—A Unification (Cambridge University Press, Cambridge, 2000)

  2. C.E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948); see also: C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (University of Illinois, Urbana, 1949)

  3. S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79 (1951); see also: S. Kullback, Information Theory and Statistics (Wiley, New York, 1959)

  4. Abramson N.: Information Theory and Coding. McGraw-Hill, New York (1963)

    Google Scholar 

  5. R.F. Nalewajski, Information Theory of Molecular Systems (Elsevier, Amsterdam, 2006) and refs. therein; R.F. Nalewajski, Use of fisher information in quantum chemistry, Int. J. Quantum Chem. (K. Jankowski issue) (in press)

  6. Nalewajski R.F.: J. Phys. Chem. A 104, 11940 (2000)

    Article  CAS  Google Scholar 

  7. Nalewajski R.F.: Mol. Phys. 102(531), 547 (2004)

    Article  CAS  Google Scholar 

  8. Nalewajski R.F.: Mol. Phys. 103, 451 (2005)

    Article  CAS  Google Scholar 

  9. R.F. Nalewajski, Mol. Phys. 104, 493, 1977, 2533 (2006)

  10. Nalewajski R.F.: Mol. Phys. 104, 365 (2006)

    Article  CAS  Google Scholar 

  11. Nalewajski R.F.: Struct. Chem. 15, 391 (2004)

    Article  CAS  Google Scholar 

  12. Nalewajski R.F.: J. Math. Chem. 38, 43 (2005)

    Article  CAS  Google Scholar 

  13. Nalewajski R.F.: Theor. Chem. Acc. 114, 4 (2005)

    Article  CAS  Google Scholar 

  14. R.F. Nalewajski, K. Jug, in: Reviews of Modern Quantum Chemistry: A Celebration of the Contributions of Robert G. Parr, vol. I, ed. by K.D. Sen (World Scientific, Singapore, 2002), p. 148

  15. Nalewajski R.F.: Chem. Phys. Lett. 386, 265 (2004)

    Article  CAS  Google Scholar 

  16. R.F. Nalewajski, J. Math. Chem. (in press), doi:10.1007/s10910-007-9345-4

  17. R.F. Nalewajski, Mol. Phys. 104, 2533, 3339 (2006)

    Google Scholar 

  18. Nalewajski R.F.: J. Phys. Chem. A 111, 4855 (2007)

    Article  CAS  Google Scholar 

  19. Nalewajski R.F.: J. Math. Chem. 43, 265 (2008)

    Article  CAS  Google Scholar 

  20. Nalewajski R.F.: J. Math. Chem. 43, 780 (2008)

    Article  CAS  Google Scholar 

  21. R.F. Nalewajski, J. Math. Chem. (in press), doi:10.1007/s10910-007-9318-7

  22. W. Heitler, F. London, Z. Physik 44, 455 (1927); for an English translation see: H. Hettema, Quantum Chemistry Classic Scientific Paper (World Scientific, Singapore, 2000); F. London, Z. Phys. 455, 46 (1928)

  23. Hirshfeld F.L.: Theor. Chim. Acta. (Berl.) 44, 129 (1977)

    Article  CAS  Google Scholar 

  24. Nalewajski R.F., Broniatowska E.: Theor. Chem. Acc. 117, 7 (2007)

    Article  CAS  Google Scholar 

  25. Nalewajski R.F., Broniatowska E.: J. Phys. Chem. A 107, 6270 (2003)

    Article  CAS  Google Scholar 

  26. R.F. Nalewajski, J. Math. Chem. (in press), doi:10.1007/s10910-008-9385-4

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30-060, Cracow, Poland

    Roman F. Nalewajski

Authors
  1. Roman F. Nalewajski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roman F. Nalewajski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nalewajski, R.F. Manifestations of Pauli exclusion principle in communication-theory of the chemical bond. J Math Chem 45, 776–789 (2009). https://doi.org/10.1007/s10910-008-9380-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-008-9380-9

Keywords

Search

Navigation